Question

The areas of two similar triangles are 16cm square and 36 cm square if the altitudes are in the ratio 2:x then find x

Answer 1

Consider two triangles ABC and PQR with AM and PN as altitudes respectively.
area of triangle ABC  = 16
area of triangle PQR     36
We know area of triangle1/ area of triangle2 = sq. of ratios of proportional sides. 
So we will get BC/QR = root of 16/36 = 4/6=2/3                   eq 1 
now we got the ratio of sides. 
In triangle ABC, are = BC x AM x 1/2                eq 2
In triangle PQR, are = QR x PN x 1/2                eq 3
We know that the ratio of area of ABC/ are of PQR is 16/36 and the side BC/QR =2/3
are of ABC = BC x AM x 1/2  = 16
are of PQR    QR x PN x 1/2     36

=2AM = 16                      since BC = 2
  3PN     36                               QR    3
 further after solving you will get 
AM = 2
PN    3 
Therefore x=3